Finite Group Databasebeta

C2×#21425294 #28616147

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21425294

Splittings

FittingC22×#106×C59 ⋊ C2
SylowC59 ⋊ C2×#2035

Subgroups

subgroupG/H
centerC24D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC22×#106×C59C2
socleC24×C59C2×D4
prime radicalC24×D59D4
hypercenterC22×#106D59
hypocenterC59C2×#2035
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#106

1662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 197026);